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Poisson-Kingman partitions

Probability 2007-05-23 v1 Combinatorics

Abstract

This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable subordinator. Applications are made to the random partition generated by the lengths of excursions of a Brownian motion or Brownian bridge conditioned on its local time at zero.

Keywords

Cite

@article{arxiv.math/0210396,
  title  = {Poisson-Kingman partitions},
  author = {Jim Pitman},
  journal= {arXiv preprint arXiv:math/0210396},
  year   = {2007}
}

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34 pages